Analysis of structural discontinuities in ship hull using finite element method

Abstract

The finite element method (FEM) is at present firmly established as a powerful and popular numerical analysis technique for finding approximate solutions to a wide range of problems in structural mechanics. Ship structures consist of various plates. Plane stress and plane strain analysis of these plates are very important. Configuring the plate type structures especially with discontinuities is one of the most important topics in the construction of not only ships but also for aircrafts and many other structures. Whenever the cross section of a structural member changes suddenly, a structural discontinuity arises, e.g. deck openings like hatch and machinery openings, access openings on side wall, cutout in the web plate, and cracks, usually a result of material imperfections or areas of high stress. This thesis concerns mainly with the fundamentals of FEM for solving plane stress and plane strain problems to analyze stresses like normal stress, shear stress and von-mises stress at the four integration points and displacements at nodes for different sections of ship structures such as plate with holes, plate with bracket and holes, and plate with fillets. Object Oriented Programming technique has been used to develop a finite element program in C++ for four node quadrilateral elements to analyze the structural discontinuity problems for various ship structures. The analysis results of gauss point stresses and nodal displacements for different models obtained from the developed program are validated with the help of commercial finite element analysis software SIMULIA ABAQUS. A mesh viewer program is also developed using the PYTHON programming language to view the generated mesh for analysis by the developed program. Fracture mechanics problem is performed for a two-dimensional plane strain single edge crack to determine the elastic fracture parameter, i.e., stress intensity factor based on stress distribution along the crack ligament. The value of stress intensity factor from the computational analysis is compared with the value obtained from the empirical formula. The typical stress distribution curve along the crack ligament has also been shown.